On the quasi-everywhere regularity of the local time of one-dimensional diffusion process in Besov space

Xicheng Zhang

doi:10.1016/S0167-7152(01)00033-5

On the quasi-everywhere regularity of the local time of one-dimensional diffusion process in Besov space

Xicheng Zhang^*

^*Corresponding author for this work

Huazhong University of Science and Technology

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

In this paper, we prove that the local time L(t,x) of one-dimensional diffusion process exists except for a set of (2,n) zero capacity for all n≥1. Moreover, we also prove that L(t,x) as a function of x∈R quasi-everywhere belongs to Besov spaces B_p,1^α for α<1/2,1<p<∞.

Original language	English
Pages (from-to)	161-169
Number of pages	9
Journal	Statistics and Probability Letters
Volume	54
Issue number	2
DOIs	https://doi.org/10.1016/S0167-7152(01)00033-5
Publication status	Published - 15 Sept 2001
Externally published	Yes

Keywords

60H10
60J55
Besov spaces
Capacity
Local times
n -parameter Ornstein-Uhlenbeck process

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10.1016/S0167-7152(01)00033-5

Cite this

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abstract = "In this paper, we prove that the local time L(t,x) of one-dimensional diffusion process exists except for a set of (2,n) zero capacity for all n≥1. Moreover, we also prove that L(t,x) as a function of x∈R quasi-everywhere belongs to Besov spaces Bp,1α for α<1/2,1",

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N2 - In this paper, we prove that the local time L(t,x) of one-dimensional diffusion process exists except for a set of (2,n) zero capacity for all n≥1. Moreover, we also prove that L(t,x) as a function of x∈R quasi-everywhere belongs to Besov spaces Bp,1α for α<1/2,1

AB - In this paper, we prove that the local time L(t,x) of one-dimensional diffusion process exists except for a set of (2,n) zero capacity for all n≥1. Moreover, we also prove that L(t,x) as a function of x∈R quasi-everywhere belongs to Besov spaces Bp,1α for α<1/2,1

KW - 60H10

KW - 60J55

KW - Besov spaces

KW - Capacity

KW - Local times

KW - n -parameter Ornstein-Uhlenbeck process

UR - https://www.scopus.com/pages/publications/0042349762

U2 - 10.1016/S0167-7152(01)00033-5

DO - 10.1016/S0167-7152(01)00033-5

M3 - Article

AN - SCOPUS:0042349762

SN - 0167-7152

VL - 54

SP - 161

EP - 169

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 2

ER -

On the quasi-everywhere regularity of the local time of one-dimensional diffusion process in Besov space

Abstract

Keywords

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